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(A) Step $1$: Evaluate statement $p$.$2$ is indeed an even prime number. So,$p$ is True $(T)$.Step $2$: Evaluate statement $q$.Given $z_1 = 2 - i$ and

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$(p \rightarrow q) \leftrightarrow (q \wedge r)$

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(A) Step $1$: Evaluate statement $p$.$2$ is indeed an even prime number. So,$p$ is True $(T)$.Step $2$: Evaluate statement $q$.Given $z_1 = 2 - i$ and $z_2 = -2 + i$,then $\bar{z}_2 = -2 - i$.$z_1 \bar{z}_2 = (2 - i)(-2 - i) = -4 - 2i + 2i + i^2 = -4 - 1 = -5$.Then $\frac{1}{z_1 \bar{z}_2} = \frac{1}{-5} = -\frac{1}{5} + 0i$.The imaginary part $\operatorname{Im}\left[\frac{1}{z_1 \bar{z}_2}ight] = 0$.Since $0 
eq -\frac{1}{5}$,statement $q$ is False $(F)$.Step $3$: Evaluate statement $r$.$	an(-945^{\circ}) = -	an(945^{\circ}) = -	an(2 	imes 360^{\circ} + 225^{\circ}) = -	an(225^{\circ}) = -	an(180^{\circ} + 45^{\circ}) = -	an(45^{\circ}) = -1$.So,$r$ is True $(T)$.Step $4$: Check the options.$p = T, q = F, r = T$.$(A)$ $(T$ $ightarrow F) \leftrightarrow (F \wedge T)$ $\Rightarrow F \leftrightarrow F = T$.$(B)$ $F \leftrightarrow T = F$.$(C)$ $T ightarrow F = F$.$(D)$ $(T$ $ightarrow T) \leftrightarrow F$ $\Rightarrow T \leftrightarrow F = F$.Thus,the correct option is $(A)$.

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Consider the following statements:$p: 2$ is an even prime number.$q: \text{If } z_1 = 2 - i, z_2 = -2 + i \text{ where } i = \sqrt{-1}, \text{ then } \operatorname{Im}\left[\frac{1}{z_1 \bar{z}_2}\right] = -\frac{1}{5}$.$r: \tan(-945^{\circ}) = -1$.Which of the following has a truth value of True?